274 research outputs found
Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part II: Stochastic Hopf Bifurcation
The spectrum of the generator (Kolmogorov operator) of a diffusion process,
referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed
characterization of correlation functions and power spectra of stochastic
systems via decomposition formulas in terms of RP resonances. Stochastic
analysis techniques relying on the theory of Markov semigroups for the study of
the RP spectrum and a rigorous reduction method is presented in Part I. This
framework is here applied to study a stochastic Hopf bifurcation in view of
characterizing the statistical properties of nonlinear oscillators perturbed by
noise, depending on their stability. In light of the H\"ormander theorem, it is
first shown that the geometry of the unperturbed limit cycle, in particular its
isochrons, is essential to understand the effect of noise and the phenomenon of
phase diffusion. In addition, it is shown that the spectrum has a spectral gap,
even at the bifurcation point, and that correlations decay exponentially fast.
Explicit small-noise expansions of the RP eigenvalues and eigenfunctions are
then obtained, away from the bifurcation point, based on the knowledge of the
linearized deterministic dynamics and the characteristics of the noise. These
formulas allow one to understand how the interaction of the noise with the
deterministic dynamics affect the decay of correlations. Numerical results
complement the study of the RP spectrum at the bifurcation, revealing useful
scaling laws. The analysis of the Markov semigroup for stochastic bifurcations
is thus promising in providing a complementary approach to the more geometric
random dynamical system approach. This approach is not limited to
low-dimensional systems and the reduction method presented in part I is applied
to a stochastic model relevant to climate dynamics in part III
Short Warm Distribution Tails Accelerate the Increase of Humid-Heat Extremes Under Global Warming
Humid-heat extremes threaten human health and are increasing in frequency with global warming, so elucidating factors affecting their rate of change is critical. We investigate the role of wet-bulb temperature (TW) frequency distribution tail shape on the rate of increase in extreme TW threshold exceedances under 2°C global warming. Results indicate that non-Gaussian TW distribution tails are common worldwide across extensive, spatially coherent regions. More rapid increases in the number of days exceeding the historical 95th percentile are projected in locations with shorter-than-Gaussian warm side tails. Asymmetry in the specific humidity distribution, one component of TW, is more closely correlated with TW tail shape than temperature, suggesting that humidity climatology strongly influences the rate of future changes in TW extremes. Short non-Gaussian TW warm tails have notable implications for dangerous humid-heat in regions where current-climate TW extremes approach human safety limits
High dimensional decision dilemmas in climate models
An important source of uncertainty in climate models is linked to the calibration of model parameters. Interest in systematic and automated parameter optimization procedures stems from the desire to improve the model climatology and to quantify the average sensitivity associated with potential changes in the climate system. Building upon on the smoothness of the response of an atmospheric circulation model (AGCM) to changes of four adjustable parameters, Neelin et al. (2010) used a quadratic metamodel to objectively calibrate the AGCM. The metamodel accurately estimates global spatial averages of common fields of climatic interest, from precipitation, to low and high level winds, from temperature at various levels to sea level pressure and geopotential height, while providing a computationally cheap strategy to explore the influence of parameter settings. Here, guided by the metamodel, the ambiguities or dilemmas related to the decision making process in relation to model sensitivity and optimization are examined. Simulations of current climate are subject to considerable regional-scale biases. Those biases may vary substantially depending on the climate variable considered, and/or on the performance metric adopted. Common dilemmas are associated with model revisions yielding improvement in one field or regional pattern or season, but degradation in another, or improvement in the model climatology but degradation in the interannual variability representation. Challenges are posed to the modeler by the high dimensionality of the model output fields and by the large number of adjustable parameters. The use of the metamodel in the optimization strategy helps visualize trade-offs at a regional level, e.g., how mismatches between sensitivity and error spatial fields yield regional errors under minimization of global objective functions
El Niño Dynamics
Bringer of storms and droughts, the El Niño∕Southern Oscillation results from the complex, sometimes chaotic interplay of ocean and atmosphere
El Niño Dynamics
Bringer of storms and droughts, the El Niño∕Southern Oscillation results from the complex, sometimes chaotic interplay of ocean and atmosphere
Universality of rain event size distributions
We compare rain event size distributions derived from measurements in
climatically different regions, which we find to be well approximated by power
laws of similar exponents over broad ranges. Differences can be seen in the
large-scale cutoffs of the distributions. Event duration distributions suggest
that the scale-free aspects are related to the absence of characteristic scales
in the meteorological mesoscale.Comment: 16 pages, 10 figure
Recent Advances Concerning Certain Class of Geophysical Flows
This paper is devoted to reviewing several recent developments concerning
certain class of geophysical models, including the primitive equations (PEs) of
atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for
large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes
equations coupled to the heat convection by adopting the Boussinesq and
hydrostatic approximations, while the tropical atmosphere model considered here
is a nonlinear interaction system between the barotropic mode and the first
baroclinic mode of the tropical atmosphere with moisture.
We are mainly concerned with the global well-posedness of strong solutions to
these systems, with full or partial viscosity, as well as certain singular
perturbation small parameter limits related to these systems, including the
small aspect ratio limit from the Navier-Stokes equations to the PEs, and a
small relaxation-parameter in the tropical atmosphere model. These limits
provide a rigorous justification to the hydrostatic balance in the PEs, and to
the relaxation limit of the tropical atmosphere model, respectively. Some
conditional uniqueness of weak solutions, and the global well-posedness of weak
solutions with certain class of discontinuous initial data, to the PEs are also
presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523
Tropical air-sea interaction in general circulation models
An intercomparison is undertaken of the tropical behavior of 17 coupled ocean-atmosphere models in which at least one component may be termed a general circulation model (GCM). The aim is to provide a taxonomy—a description and rough classification—of behavior across the ensemble of models, focusing on interannual variability. The temporal behavior of the sea surface temperature (SST) field along the equator is presented for each model, SST being chosen as the primary variable for intercomparison due to its crucial role in mediating the coupling and because it is a sensitive indicator of climate drift. A wide variety of possible types of behavior are noted among the models. Models with substantial interannual tropical variability may be roughly classified into cases with propagating SST anomalies and cases in which the SST anomalies develop in place. A number of the models also exhibit significant drift with respect to SST climatology. However, there is not a clear relationship between climate drift and the presence or absence of interannual oscillations. In several cases, the mode of climate drift within the tropical Pacific appears to involve coupled feedback mechanisms similar to those responsible for El Niño variability. Implications for coupled-model development and for climate prediction on seasonal to interannual time scales are discussed. Overall, the results indicate considerable sensitivity of the tropical coupled ocean-atmosphere system and suggest that the simulation of the warm-pool/cold-tongue configuration in the equatorial Pacific represents a challenging test for climate model parameterizations
Global-scale climate impact functions: the relationship between climate forcing and impact
Although there is a strong policy interest in the impacts of climate change corresponding to different degrees of climate change, there is so far little consistent empirical evidence of the relationship between climate forcing and impact. This is because the vast majority of impact assessments use emissions-based scenarios with associated socio-economic assumptions, and it is not feasible to infer impacts at other temperature changes by interpolation. This paper presents an assessment of the global-scale impacts of climate change in 2050 corresponding to defined increases in global mean temperature, using spatially-explicit impacts models representing impacts in the water resources, river flooding, coastal, agriculture, ecosystem and built environment sectors. Pattern-scaling is used to construct climate scenarios associated with specific changes in global mean surface temperature, and a relationship between temperature and sea level used to construct sea level rise scenarios. Climate scenarios are constructed from 21 climate models to give an indication of the uncertainty between forcing and response. The analysis shows that there is considerable uncertainty in the impacts associated with a given increase in global mean temperature, due largely to uncertainty in the projected regional change in precipitation. This has important policy implications. There is evidence for some sectors of a non-linear relationship between global mean temperature change and impact, due to the changing relative importance of temperature and precipitation change. In the socio-economic sectors considered here, the relationships are reasonably consistent between socio-economic scenarios if impacts are expressed in proportional terms, but there can be large differences in absolute terms. There are a number of caveats with the approach, including the use of pattern-scaling to construct scenarios, the use of one impacts model per sector, and the sensitivity of the shape of the relationships between forcing and response to the definition of the impact indicator
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